Bennett, Colin (1973) A HausdorffYoung theorem for rearrangementinvariant spaces. Pacific Journal of Mathematics, 47 (2). pp. 311328. ISSN 00308730. http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73

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Abstract
The classical HausdorffYoung theorem is extended to the setting of rearrangementinvariant spaces. More precisely, if 1 <_ p <_ 2, p[1] + q[1] = 1, and if X is a rearrangementinvariant space on the circle T with indices equal to p[1], it is shown that there is a rearrangementinvariant space X on the integers Z with indices equal to q[1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangementinvariant space Y on Z with indices equal to q[1], 2 < q <__ oo, there is a rearrangementinvariant space Y on T with indices equal to p[1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr].
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Record Number:  CaltechAUTHORS:BENpjm73 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:BENpjm73 
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ID Code:  554 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  18 Aug 2005 
Last Modified:  26 Dec 2012 08:40 
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